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Epic Epic HeavisideTheta problem

  • To: mathgroup at smc.vnet.net
  • Subject: [mg108882] Epic Epic HeavisideTheta problem
  • From: Sean McConnell <smcconne at physi.uni-heidelberg.de>
  • Date: Mon, 5 Apr 2010 08:02:47 -0400 (EDT)

Hi all,

I have encountered what I think is some sort of a serious problem with
HeavisideTheta[]. Essentially I am using HeavisideTheta[] to switch on
and switch off a simple (sinusoidal) blending function that is applied
to the small and large z approximations of a Hypergeometric1F1[a,b,z] in
order to get an analytic approximation to its indefinite integral.
Obviously if the small approximation is not switched off at some point
then the approximation explodes, and with it the integral. 

My thoughts are that somehow the small z approximation is finding a way
to overpower HeavisideTheta[] and insert its unwanted behaviour into my
integral after the point at which it should have been switched off,
because the integral appears quite nice up to a certain point, but after
this point becomes highly oscillatory with an increasing amplitude to
boot.

I have also tried other alternatives like Piecewise[] but alas
Mathematica for some reason no longer wants to attempt the integral when
there is a Piecewise involved.

Any help regarding how one can make my problem go away would be greatly
appreciated.

Thanks, Sean.





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